POST UTME OAU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a geometric sequence, the first term is 2 and the common ratio is 3. What is the sum of the first 5 terms?
A. \frac{243}{2}
B. \frac{243}{4}
C. \frac{243}{8}
D. \frac{243}{16}
Question 2
Determine the value of x in the equation \( \frac{1}{2}x + 5 = \frac{3}{4}x - 2 \).
A. \frac{11}{4}
B. \frac{3}{2}
C. -\frac{1}{2}
D. -\frac{3}{4}
Question 3
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant formula.
A. \( egin{pmatrix} 6 \ -2 \end{pmatrix} \)
B. \( egin{pmatrix} -6 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} 2 \ -6 \end{pmatrix} \)
D. \( egin{pmatrix} -2 \ 6 \end{pmatrix} \)
Question 4
Solve the system of linear equations u\sing matrices: \[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix} \]
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}
Question 5
Solve the equation \( x^3 + 2x^2 - 7x - 12 = 0 \) by factoring.
A. \( x = -3, 2, -2 \)
B. \( x = -3, 2, 4 \)
C. \( x = -3, 2, -4 \)
D. \( x = -3, 2, 1 \)
Question 6
A random variable X follows a binomial distribution with parameters n = 10 and p = 0.4. Find the probability that X is greater than 6.
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 7
Solve the inequality \( \frac{x + 2}{x - 1} > 0 \) u\sing a sign chart.
A. \( x < -2 \) or \( x > 1 \)
B. \( x < -2 \) or \( x < 1 \)
C. \( x > -2 \) or \( x > 1 \)
D. \( x < -2 \) or \( x < 1 \)
Question 8
Find the volume of the solid formed by rotating the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 9
Solve the equation \( 2^x + 2^x = 100 \).
A. x = 4
B. x = 5
C. x = 6
D. x = 7
Question 10
Find the volume of the solid formed by rotating the region bounded by $y = x^2$ and $y = 2x$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 11
A polynomial function has a degree of 4 and has zeros at x = -2, x = 3, and x = 4. What is the factored form of the polynomial?
A. \( x + 2 \)\( x - 3 \)\( x - 4 \)\( x + 1 \)
B. \( x + 2 \)\( x - 3 \)\( x - 4 \)\( x - 1 \)
C. \( x + 2 \)\( x - 3 \)\( x - 4 \)\( x + 3 \)
D. \( x + 2 \)\( x - 3 \)\( x - 4 \)\( x - 2 \)
Question 12
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. \( \frac{32}{3} \pi \)
B. \( \frac{64}{3} \pi \)
C. \( \frac{128}{3} \pi \)
D. \( \frac{256}{3} \pi \)
Question 13
A company produces two products, A and B. The profit from the sale of product A is $\frac{1}{2}$x + $\frac{1}{4}$y, and the profit from the sale of product B is $\frac{3}{4}$x - $\frac{1}{2}$y. If the company produces 100 units of product A and 50 units of product B, find the total profit.
A. $\frac{75}{2}$
B. $\frac{125}{2}$
C. $\frac{175}{2}$
D. $\frac{225}{2}
Question 14
Find the volume of the frustum of a cone with height $h$ and radii of the bases $r_1$ and $r_2$.
A. \frac{1}{3}\pi h \( r_1^2 + r_2^2 + r_1 r_2 \)
B. \frac{1}{3}\pi h \( r_1^2 + r_2^2 - r_1 r_2 \)
C. \frac{1}{3}\pi h \( r_1^2 - r_2^2 + r_1 r_2 \)
D. \frac{1}{3}\pi h \( r_1^2 - r_2^2 - r_1 r_2 \)
Question 15
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4

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